(Note: The question does imply more previous knowledge than I had assumed; however, as some of what is implied might not have been intended and my answer is already written, I'll leave everything below intact.)
You need multiple programs actually, and you should probably learn to make some simple programs yourself. That is, if the database is to be modified, or even created dynamically, by a program. Even if you don't exactly program (Database Administrator is a separate position in larger companies), the query language - most commonly a dialect of SQL - will be, in my opinion, considerably more difficult than most modern programming languages. This answer will walk you through getting a taste for web development and database administration.
It would be a good idea to first know how to write HTML, but be aware that it is currently in heavy flux; we've been going through versions very fast in recent years, not to mention the changes in the very closely related languages of CSS (now underway) and JavaScript (just completed). See the appendix at the end of the answer if you also wish to learn those.
The current version of HTML is XHTML 1.1, but XHTML 1.0 Strict is very close and I don't see any more current options, so read this tutorial:
http://heptagrama.com/how-to-make-a-web-page.htm
MySQL is the most popular database management system (DBMS), and PHP is its usual companion - not to mention the most popular server-side scripting language (SSSL) in its own right. Both are free to download, and free to be modified and redistributed subject to a few conditions. Most commonly, they will be installed on the Apache server (also the most popular project of its type), and this arrangement is known as a stack. It is pre-packaged for Windows (WAMP), Linux (LAMP), and Macintosh (MAMP). A quick search-engine query of one of these acronyms will give you links to a few options, but try to find one which offers phpMyAdmin for a smoother learning curve.
Now that you have a "development server," you need to read up on how to use it. The central thing to learn about it, and the reason you learned HTML above, is PHP - whose syntax is fairly similar to that of JavaScript:
http://www.php.net/manual/en/tutorial.firstpage.php
Pick one or both of these phpMyAdmin tutorials to read through:
http://library.creativecow.net/articles/chaffin_abraham/mysql-php-basics.php
http://webdevcodex.com/tutorial-installing-apache2-php5-mysql5-phpmyadmin3-windows-7-vista/
Now that you know all these languages, you have a lot of resources you might want to bookmark; they are at http://jesdisciple.110mb.com/database.html , on my personal site because there were too many. (Exclude the CSS and JavaScript links if you didn't read the appendix.) Finally, you should find an online community, such as a message board, for each of your languages where you can ask questions.
==Appendix: CSS and JavaScript==
CSS is a stylesheet language for telling browsers how to display things on a page, while JavaScript is a programming language for interacting with the same things. (Technically JavaScript is ECMAScript, the name of the standard; JavaScript is a trademark.) CSS is more efficient while JavaScript is more versatile. As noted in the main body of this answer, both are undergoing drastic changes along with HTML; we've witnessed some particularly significant changes in JavaScript.
The upcoming HTML 5 is more similar to the style used in this CSS tutorial, but they are not very different from XHTML:
http://www.w3.org/Style/CSS/learning
Be aware that this JavaScript tutorial employs some poor practices in its examples; we don't have anything better - yet:
http://www.w3schools.com/js/default.asp
Stuff that changed in the recent ECMAScript 5:
http://ajaxian.com/archives/ecmascript-5-changes-to-javascript
References for CSS and JavaScript are included here: http://jesdisciple.110mb.com/database.html